---
title: "Predictive compaction modelling for ternary direct-compression formulations"
id: "pubmed-42546992"
canonical_url: "https://medichelpline.com/clinical-feed/pubmed-42546992"
content_type: "clinical_feed_article"
specialty: "Pharmacology"
source_name: "PubMed / NCBI"
source_url: "https://pubmed.ncbi.nlm.nih.gov/42546992/"
doi: "10.1016/j.ijpharm.2026.127253"
published_at: "2026-09-05T00:00:00.000Z"
evidence_level: "Journal Article"
license: "CC-BY-NC-4.0 / Informational Use"
---
# Predictive compaction modelling for ternary direct-compression formulations
## Provenance & Clinical Metadata
- **Canonical URL:** https://medichelpline.com/clinical-feed/pubmed-42546992
- **Specialty:** [Pharmacology](https://medichelpline.com/clinical-feed/pharmacology.md)
- **Primary Source:** PubMed / NCBI
- **Source URL:** [Original Journal Publication](https://pubmed.ncbi.nlm.nih.gov/42546992/)
- **DOI:** [10.1016/j.ijpharm.2026.127253](https://doi.org/10.1016%2Fj.ijpharm.2026.127253)
- **Published At:** 2026-09-05T00:00:00.000Z
- **Evidence Rating:** Journal Article
## Executive GIST (TL;DR)
- Direct compression formulation development is resource intensive and requires characterising compressibility and compactability across formulation space. The study extended a global optimisation of mixture rules to a **ternary formulation** space (API - brittle filler - elastic filler). - Test systems used three grades each of **paracetamol** and **ibuprofen** combined with a consistent placebo base to evaluate predictive performance across APIs and grades. - Two empirical compaction/compression models were central: the **Kawakita** model for compression behaviour and the **Ryshkewitch–Duckworth** model for tensile strength (compactibility). - The global optimisation approach outperformed traditional line-of-best-fit mixture rules, achieving strong performance for the Kawakita model (R2 > 0.94; RMSE 30% across all formulations; median API savings were 75%–95% under Acceptable and Good performance thresholds. - Savings declined as performance thresholds tightened, with the highest variability seen in ibuprofen formulations. The Kawakita model enabled reductions across all thresholds; the Ryshkewitch–Duckworth model supported reductions mainly up to the Acceptable threshold. - MBDoE did not systematically outperform random experiment selection, but the optimisation framework still offers a material-sparing way to populate empirical models for predicting **tablet porosity** and **tensile strength** of ternary blends. - Conflict of interest: financial support reported from GlaxoSmithKline R&D and Scottish Funding Council for one author; other authors declared no relevant competing interests.
## Clinical Analysis & Structured Key Points
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Epub 2026 Aug 3. # Predictive compaction modelling of ternary direct compression formulations [Theo Tait](https://pubmed.ncbi.nlm.nih.gov/?term=Tait+T&cauthor_id=42546992)[ 1 ](https://pubmed.ncbi.nlm.nih.gov/42546992/#full-view-affiliation-1 "CMAC, University of Strathclyde, Glasgow, G1 1RD, UK; Strathclyde Institute of Pharmacy & Biomedical Sciences, University of Strathclyde, Glasgow, G4 0RE, UK."), [Mohammad Salehian](https://pubmed.ncbi.nlm.nih.gov/?term=Salehian+M&cauthor_id=42546992)[ 1 ](https://pubmed.ncbi.nlm.nih.gov/42546992/#full-view-affiliation-1 "CMAC, University of Strathclyde, Glasgow, G1 1RD, UK; Strathclyde Institute of Pharmacy & Biomedical Sciences, University of Strathclyde, Glasgow, G4 0RE, UK."), [Magdalini Aroniada](https://pubmed.ncbi.nlm.nih.gov/?term=Aroniada+M&cauthor_id=42546992)[ 2 ](https://pubmed.ncbi.nlm.nih.gov/42546992/#full-view-affiliation-2 "Strathclyde Institute of Pharmacy & Biomedical Sciences, University of Strathclyde, Glasgow, G4 0RE, UK; GSK, Ware R&D, Harris' Lane, Ware, SG12 0GX, UK."), [Andrew P Shier](https://pubmed.ncbi.nlm.nih.gov/?term=Shier+AP&cauthor_id=42546992)[ 3 ](https://pubmed.ncbi.nlm.nih.gov/42546992/#full-view-affiliation-3 "GSK, Ware R&D, Harris' Lane, Ware, SG12 0GX, UK."), [Richard Elkes](https://pubmed.ncbi.nlm.nih.gov/?term=Elkes+R&cauthor_id=42546992)[ 3 ](https://pubmed.ncbi.nlm.nih.gov/42546992/#full-view-affiliation-3 "GSK, Ware R&D, Harris' Lane, Ware, SG12 0GX, UK."), [John Robertson](https://pubmed.ncbi.nlm.nih.gov/?term=Robertson+J&cauthor_id=42546992)[ 1 ](https://pubmed.ncbi.nlm.nih.gov/42546992/#full-view-affiliation-1 "CMAC, University of Strathclyde, Glasgow, G1 1RD, UK; Strathclyde Institute of Pharmacy & Biomedical Sciences, University of Strathclyde, Glasgow, G4 0RE, UK."), [Daniel Markl](https://pubmed.ncbi.nlm.nih.gov/?term=Markl+D&cauthor_id=42546992)[ 4 ](https://pubmed.ncbi.nlm.nih.gov/42546992/#full-view-affiliation-4 "CMAC, University of Strathclyde, Glasgow, G1 1RD, UK; Strathclyde Institute of Pharmacy & Biomedical Sciences, University of Strathclyde, Glasgow, G4 0RE, UK. Electronic address: daniel.markl@strath.ac.uk.") Affiliations Expand ### Affiliations * 1 CMAC, University of Strathclyde, Glasgow, G1 1RD, UK; Strathclyde Institute of Pharmacy & Biomedical Sciences, University of Strathclyde, Glasgow, G4 0RE, UK. * 2 Strathclyde Institute of Pharmacy & Biomedical Sciences, University of Strathclyde, Glasgow, G4 0RE, UK; GSK, Ware R&D, Harris' Lane, Ware, SG12 0GX, UK. * 3 GSK, Ware R&D, Harris' Lane, Ware, SG12 0GX, UK. * 4 CMAC, University of Strathclyde, Glasgow, G1 1RD, UK; Strathclyde Institute of Pharmacy & Biomedical Sciences, University of Strathclyde, Glasgow, G4 0RE, UK. Electronic address: daniel.markl@strath.ac.uk. * PMID: **42546992** * DOI: [ 10.1016/j.ijpharm.2026.127253 ](https://doi.org/10.1016/j.ijpharm.2026.127253) Free article Item in Clipboard # Predictive compaction modelling of ternary direct compression formulations Theo Tait et al. Int J Pharm. 2026. Free article Show details Display options Display options Format Abstract PubMed PMID Int J Pharm Actions * [ Search in PubMed ](https://pubmed.ncbi.nlm.nih.gov/?term=%22Int+J+Pharm%22%5Bjour%5D&sort=date&sort_order=desc) * [ Search in NLM Catalog ](https://www.ncbi.nlm.nih.gov/nlmcatalog?term=%22Int+J+Pharm%22%5BTitle+Abbreviation%5D) * [ Add to Search ](https://pubmed.ncbi.nlm.nih.gov/42546992/) . 2026 Sep 5:702:127253. doi: 10.1016/j.ijpharm.2026.127253. Epub 2026 Aug 3. ### Authors [Theo Tait](https://pubmed.ncbi.nlm.nih.gov/?term=Tait+T&cauthor_id=42546992)[ 1 ](https://pubmed.ncbi.nlm.nih.gov/42546992/#short-view-affiliation-1 "CMAC, University of Strathclyde, Glasgow, G1 1RD, UK; Strathclyde Institute of Pharmacy & Biomedical Sciences, University of Strathclyde, Glasgow, G4 0RE, UK."), [Mohammad Salehian](https://pubmed.ncbi.nlm.nih.gov/?term=Salehian+M&cauthor_id=42546992)[ 1 ](https://pubmed.ncbi.nlm.nih.gov/42546992/#short-view-affiliation-1 "CMAC, University of Strathclyde, Glasgow, G1 1RD, UK; Strathclyde Institute of Pharmacy & Biomedical Sciences, University of Strathclyde, Glasgow, G4 0RE, UK."), [Magdalini Aroniada](https://pubmed.ncbi.nlm.nih.gov/?term=Aroniada+M&cauthor_id=42546992)[ 2 ](https://pubmed.ncbi.nlm.nih.gov/42546992/#short-view-affiliation-2 "Strathclyde Institute of Pharmacy & Biomedical Sciences, University of Strathclyde, Glasgow, G4 0RE, UK; GSK, Ware R&D, Harris' Lane, Ware, SG12 0GX, UK."), [Andrew P Shier](https://pubmed.ncbi.nlm.nih.gov/?term=Shier+AP&cauthor_id=42546992)[ 3 ](https://pubmed.ncbi.nlm.nih.gov/42546992/#short-view-affiliation-3 "GSK, Ware R&D, Harris' Lane, Ware, SG12 0GX, UK."), [Richard Elkes](https://pubmed.ncbi.nlm.nih.gov/?term=Elkes+R&cauthor_id=42546992)[ 3 ](https://pubmed.ncbi.nlm.nih.gov/42546992/#short-view-affiliation-3 "GSK, Ware R&D, Harris' Lane, Ware, SG12 0GX, UK."), [John Robertson](https://pubmed.ncbi.nlm.nih.gov/?term=Robertson+J&cauthor_id=42546992)[ 1 ](https://pubmed.ncbi.nlm.nih.gov/42546992/#short-view-affiliation-1 "CMAC, University of Strathclyde, Glasgow, G1 1RD, UK; Strathclyde Institute of Pharmacy & Biomedical Sciences, University of Strathclyde, Glasgow, G4 0RE, UK."), [Daniel Markl](https://pubmed.ncbi.nlm.nih.gov/?term=Markl+D&cauthor_id=42546992)[ 4 ](https://pubmed.ncbi.nlm.nih.gov/42546992/#short-view-affiliation-4 "CMAC, University of Strathclyde, Glasgow, G1 1RD, UK; Strathclyde Institute of Pharmacy & Biomedical Sciences, University of Strathclyde, Glasgow, G4 0RE, UK. Electronic address: daniel.markl@strath.ac.uk.") ### Affiliations * 1 CMAC, University of Strathclyde, Glasgow, G1 1RD, UK; Strathclyde Institute of Pharmacy & Biomedical Sciences, University of Strathclyde, Glasgow, G4 0RE, UK. * 2 Strathclyde Institute of Pharmacy & Biomedical Sciences, University of Strathclyde, Glasgow, G4 0RE, UK; GSK, Ware R&D, Harris' Lane, Ware, SG12 0GX, UK. * 3 GSK, Ware R&D, Harris' Lane, Ware, SG12 0GX, UK. * 4 CMAC, University of Strathclyde, Glasgow, G1 1RD, UK; Strathclyde Institute of Pharmacy & Biomedical Sciences, University of Strathclyde, Glasgow, G4 0RE, UK. Electronic address: daniel.markl@strath.ac.uk. * PMID: **42546992** * DOI: [ 10.1016/j.ijpharm.2026.127253 ](https://doi.org/10.1016/j.ijpharm.2026.127253) Item in Clipboard Full text links Cite Display options Display options Format Abstract PubMed PMID ## Abstract Developing directly-compressed formulations remains a resource-intensive task, requiring substantial experimental effort to characterise the compressibility and compactability of a formulation space. This study extends a global optimisation of mixture rules to a ternary formulation space (API-brittle filler-elastic filler) and investigates the potential for reducing experimental burden whilst maintaining the predictive accuracy of empirical compression and compaction models. Three grades each of paracetamol and ibuprofen, combined with a consistent placebo base, were used to evaluate the approach. The global optimisation outperformed the traditional line of best fit approach, achieving strong predictive performance for the Kawakita model (R2>0.94; RMSE<0.01) and more variable fits for the Ryshkewitch-Duckworth model (R2 = 0.93 - 0.95 and RMSE = 0.23 - 0.39 MPa for paracetamol; R2 = 0.70 - 0.83 and RMSE = 0.31 - 0.37 MPa for ibuprofen). The optimisations performance was found to improve when the training dataset considered only drug-loaded blends. The exploration of reducing experimental burden considered a Model-Based Design of Experiments (MBDoE) which was benchmarked against random experiment selection. Integrating MBDoE with optimised mixture rules reduced API consumption by over 30% across all formulations, with median savings of 75%-95% under Acceptable and Good performance thresholds. Savings decreased with increasing threshold stringency, with the greatest variability observed in ibuprofen formulations. The Kawakita model supported reductions across all threshold levels, whilst the Ryshkewitch-Duckworth model showed limited capacity beyond the Acceptable threshold. The MBDoE did not outperform the random selection of experiments, however the optimisation framework for populating empirical compression and compaction models offers a resource-efficient approach to predicting tablet porosity and tensile strength of ternary API loaded blends. **Keywords:** Direct compression; Oral solid doses; Predictive models; Ternary mixtures. Copyright © 2026 The Authors. Published by Elsevier B.V. All rights reserved. [PubMed Disclaimer](https://pubmed.ncbi.nlm.nih.gov/disclaimer/) ## Conflict of interest statement Declaration of competing interest The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Daniel Markl reports financial support was provided by GlaxoSmithKline Research & Development Limited. Daniel Markl reports financial support was provided by Scottish Funding Council. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ## Similar articles * [ Empirical Model Variability: Developing a new global optimisation approach to populate compression and compaction mixture rules. ](https://pubmed.ncbi.nlm.nih.gov/39019299/) Tait T, Salehian M, Aroniada M, Shier AP, Elkes R, Robertson J, Markl D.Tait T, et al.Int J Pharm. 2024 Sep 5;662:124475. doi: 10.1016/j.ijpharm.2024.124475. Epub 2024 Jul 15.Int J Pharm. 2024.PMID: 39019299 * [ An interaction-based mixing model for predicting porosity and tensile strength of directly compressed ternary blends of pharmaceutical powders. ](https://pubmed.ncbi.nlm.nih.gov/39147250/) Corrigan J, Li F, Dawson N, Reynolds G, Bellinghausen S, Zomer S, Litster J.Corrigan J, et al.Int J Pharm. 2024 Oct 25;664:124587. doi: 10.1016/j.ijpharm.2024.124587. Epub 2024 Aug 13.Int J Pharm. 2024.PMID: 39147250 * [ Predicting the compressibility and compactibility profiles of pharmaceutical active ingredients for design of multi-component tablets. ](https://pubmed.ncbi.nlm.nih.gov/42177921/) Cheng C, Wang K, Schlindwein W, Crean C, Wu CY, He Z, Liu X, Li M.Cheng C, et al.Int J Pharm. 2026 Jun 25;699:127000. doi: 10.1016/j.ijpharm.2026.127000. Epub 2026 May 23.Int J Pharm. 2026.PMID: 42177921 * [ An integrated material-sparing method for determining dilution potential of direct compression tablet fillers. ](https://pubmed.ncbi.nlm.nih.gov/41448738/) Tharanon W, Guo Y, Peerapattana J, Sun CC.Tharanon W, et al.J Pharm Sci. 2025 Dec;114(12):104061. doi: 10.1016/j.xphs.2025.104061. Epub 2025 Dec 23.J Pharm Sci. 2025.PMID: 41448738 * [ Evaluation of two novel co-processed excipients for direct compression of orodispersible tablets and mini-tablets. ](https://pubmed.ncbi.nlm.nih.gov/34474110/) Kokott M, Lura A, Breitkreutz J, Wiedey R.Kokott M, et al.Eur J Pharm Biopharm. 2021 Nov;168:122-130. doi: 10.1016/j.ejpb.2021.08.016. Epub 2021 Aug 30.Eur J Pharm Biopharm. 2021.PMID: 34474110 [ See all similar articles ](https://pubmed.ncbi.nlm.nih.gov/?linkname=pubmed_pubmed&from_uid=42546992) ## MeSH terms * Acetaminophen* / chemistry Actions * [ Search in PubMed ](https://pubmed.ncbi.nlm.nih.gov/?term=%22Acetaminophen%2Fchemistry%22%5BMAJR%5D&sort=date&sort_order=desc) * [ Search in MeSH ](https://www.ncbi.nlm.nih.gov/mesh?term=Acetaminophen) * [ Add to Search ](https://pubmed.ncbi.nlm.nih.gov/42546992/) * Bulk Drugs Actions * [ Search in PubMed ](https://pubmed.ncbi.nlm.nih.gov/?term=%22Bulk+Drugs%22%5BMeSH%5D&sort=date&sort_order=desc) * [ Search in MeSH ](https://www.ncbi.nlm.nih.gov/mesh?term=Bulk+Drugs) * [ Add to Search ](https://pubmed.ncbi.nlm.nih.gov/42546992/) * Chemistry, Pharmaceutical / methods Actions * [ Search in PubMed ](https://pubmed.ncbi.nlm.nih.gov/?term=%22Chemistry%2C+Pharmaceutical%2Fmethods%22%5BMeSH%5D&sort=date&sort_order=desc) * [ Search in MeSH ](https://www.ncbi.nlm.nih.gov/mesh?term=Chemistry%2C+Pharmaceutical) * [ Add to Search ](https://pubmed.ncbi.nlm.nih.gov/42546992/) * Drug Compounding* / methods Actions * [ Search in PubMed ](https://pubmed.ncbi.nlm.nih.gov/?term=%22Drug+Compounding%2Fmethods%22%5BMAJR%5D&sort=date&sort_order=desc) * [ Search in MeSH ](https://www.ncbi.nlm.nih.gov/mesh?term=Drug+Compounding) * [ Add to Search ](https://pubmed.ncbi.nlm.nih.gov/42546992/) * Ibuprofen* / chemistry Actions * [ Search in PubMed ](https://pubmed.ncbi.nlm.nih.gov/?term=%22Ibuprofen%2Fchemistry%22%5BMAJR%5D&sort=date&sort_order=desc) * [ Search in MeSH ](https://www.ncbi.nlm.nih.gov/mesh?term=Ibuprofen) * [ Add to Search ](https://pubmed.ncbi.nlm.nih.gov/42546992/) * Tablets Actions * [ Search in PubMed ](https://pubmed.ncbi.nlm.nih.gov/?term=%22Tablets%22%5BMeSH%5D&sort=date&sort_order=desc) * [ Search in MeSH ](https://www.ncbi.nlm.nih.gov/mesh?term=Tablets) * [ Add to Search ](https://pubmed.ncbi.nlm.nih.gov/42546992/) ## Substances * Acetaminophen Actions * [ Search in PubMed ](https://pubmed.ncbi.nlm.nih.gov/?term=%22Acetaminophen%22%5Bnm%5D&sort=date&sort_order=desc) * [ Search in MeSH ](https://www.ncbi.nlm.nih.gov/mesh?term=%22Acetaminophen%22)
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